Just a take here as a literal black guy, or I guess a general story about my experiences, and some recommendations for white or non-black people in general.
When I first started MUing, I played exclusively white characters because when I was younger I had some internal racial issues that I hadn't worked out yet, and my previous experiences irl led me to believe that people simply wouldn't want to play with me because of the race of my character, and I also hid my irl race, which was easy because everyone naturally assumes that you're white on the internet if you don't say otherwise.
That said, I have on quite a lot of occasions across quite a few MUs experience people wanting to RP with my black characters less than others. Could be the culture I was in, could be that the characters coincidentally weren't as good as my others, but it is an experience I have 100% had and noticed, and in games like that I usually just drop the black character and end up getting a white one, mostly just because I don't feel like the frustration on an OOC level. They aren't really feelings I come to RP to have. And just to reassure you, this is not a common experience, just a few places I've been in.
There's also various things I've noticed just off-handedly. Like on Arx how there's literally a rule saying you can't just straight up race swap a character, and it happens there all the time. Pretty much characters get pretty drastically shifted away from their description when it comes to racial stuff. But, that said, Arx is still more diverse than the average MUSH I've played, that's just a minor racial peeve I have with the overall culture of PB selection there.
I have indeed many times played a white character as my first alt on a MUSH because I just felt it would be easier to acclimate myself and get a feel for the game, and I always have a bit of an OOC anxiety that I'll have to deal with some nonsense or people fetishing up my pages (it's definitely happened before). I feel that I need to trust a MU on some level before I can play a black character there, which I know sounds weird, but as I said, I just don't go to a MU to feel the same things I do on an OOC level. If I'm gonna play a black character I just like to know that it's "safe" to do so. That the people around me are gonna be cool.
The word microaggression gets thrown around a lot, but holy shit does playing a black character flip on that switch on an OOC level if you're somewhere people just don't know how to act.
As far as white people playing black characters (I don't wanna speak for any race here, just mine from my own perspective), I think it's totally cool as long as it's not some crazy shit like on Shang where people take that as a bizarre license to say the N word and all kinds of stereotypical shit as loudly as possible (this shit has definitely happened in Shang's square, when I used to play that MU years ago).
When it comes to worrying about being accidentally offensive, I'd say that if you're a generally mindful person it probably won't be that big of a deal. For the most part you can play a black person more or less how you'd play a white character, there's just little differences like the way we have to deal with our hair or how we might approach certain situations on a cultural level. But there are all kind of quick research things if you're ever unsure. Or hell I have literally nothing against answering questions like that, as I really don't generally find sincere questions to be offensive when I know you're really trying to learn something.
I'd say that Doctor Who (well I've only seen up to Capaldi, I'm behind still) is a great example of how to handle black characters. Hell, Martha being black only really comes up a few times in the whole series, as there's just more important and interesting shit than her race going on. And the one time I do remember it coming up was in a historical context that was done really well. Or hell even the way black characters are handled in the MCU, as they show just how diverse people can be within the same race. And if you really want some extra credit, watch Living Single (great for seeing the diversity of both black men and women as just normal ass people), Fresh Prince (posh ass black people), or every season of A Different World except the first season (the first season is Bill Cosby's trash ass season, just skip it entirely). And if you want more modern stuff, Black'ish is great (even though they had Chris Brown on one episode which I'm still wtf about), as it really captures a lot of very minor nuances about black culture. And Jordan Peele's modern work seems to be on point (probably skip Key & Peele for inspiration. It's a show I love but it's a cultural minefield).
I know this is getting a bit lengthy, but just let me name a few probably unlikely and unexpected pieces of media that I just don't think are good to take inspiration from.
Family Matters, while I really genuinely love Family Matters (Urkel), it has some pretty questionable politics when it comes to cops and stuff. It does try to address cops and race and all that, but I just don't think it's a good reference point if you're already going in confused. Plus it's got a lot of that bizarre borderline conservative Christian values thing going on like a lot of shows from back then (Fresh Prince does that to a far lesser extent and actually stops doing that at some point). And The Cosby Show, like, the fact that no one should be watching Bill Cosby to begin with, Cosby's work often had this very judgmental wag your finger at not being a "proper" black person thing to it. It's the same reason I say skip the first season of A Different World, as it stops being his show after that.
Also, never Tyler Perry. Never any Tyler Perry, ever. Also no Wayans' Brothers movies or shows (even though I love them).
You also might be noticing that I didn't really list dramas and stuff. But that's almost entirely because dramas get super bogged down in a way where I just often find the portrayals of black people to just be far too heavy handed. A Different World and Black'Ish do handle some pretty serious issues, but I just can't in good faith recommend a drama outside of Jordan Peele's work. Luke Cage on Netflix might also work pretty well, has a nice balance on characterization.
Man who remembers when I used to write these spammy ass posts on WORA? Hopefully this is helpful rather than nonsense.
Now I'm tempted to play a black characer on Arx, as I've been thinking of an OC. I do play a POC in general on Arx, Theo. So far that's been pretty chill.
@Rinel Also excuse me, I totally tried to bang Rinel.